My (m36) new girlfriend (f33) holds an ex partner as a close friend.

As the title shows, my girlfriend since Feb this year holds an ex as a close friend. This wasn't a problem for me but the dynamics around this are starting to make me a little uncomfortable for the following reasons. She is from another country and will go home maybe 2 to 3 times a year, where her ex is. She recently went back and spent a lot of time with him. At the time I did not know he was an ex, only finding this out when she returned. When I queried if this was something she felt I should have known, regardless of how platonic she sees it, she agreed and said she didnt consider it as she doesnt see him in anyway other than a friend.

After ironing this out, I understood her and trusted her. Fast forward to this week and she, unprompted, gave me the code to access her phone - today she said she would be in the shower and was expecting a call so I could go ahead and answer it for her. The burden of having her code to the phone is not something I wanted or would ever ask for but in line with being open and on the same page I accepted. So instead of a call the person she was expecting sent a message, this opened up her WhatsApp and I saw her exs name, I was faced with breaking her trust to open their conversation or just shutting my eyes to it. In a weak moment I opened the conversation and scrolled, it was general back and forth and was clear they had met a lot when she was out there, which again I am okay with based on her evaluation and reassurance of the situation. However one message stood out to me, he sent a message which I am still unsure of how to interpret, even with context of him being a friend.

His very last message sent was 'Make time for us when we are back' - initially I thought okay maybe the use of 'us' and 'we' was to indicate there was a group of people coming back from somewhere and he was letting her know she needed to make time to see them. But as my mind has gone over and over the message, it would seem like in the worst case scenario his language and insinuation in this message was something that conveys more than friends, even if not a relationship I feel uneasy at this message. Her response was in a her native language and in my panic I cannot remember the exact wording but it was to the effect of 'in 1 hour'.

That was the last message between them for over 2 weeks now, since she has been back in from her trip home. My question is, not so much the situation, but my reaction to it, the fact I felt compelled to read the messages and not just trust her, am I ready for a serious relationship with this person if this is how I act. I am upset with myself that I broke her trust in reading her personal messages and that alone doesnt sit right with me.

Alongside this, a part of me does feel I acted on my slight doubts at what is essentially my gf spending a lot of time with her ex, who neglected to tell me he was an ex until she returned and what could be meant of that message from him, it seems very personal no matter the context. Added to the fact she will regularly go home and this situation will still be very much alive and something I have to contend with knowing when she is away and im seeking some understanding.

For additional context, we have recently had a big talk about ex's and boundaries in a relationship and I feel bring this up almost a day later, not only will show my lack of trust by reading her messages but also will bring up something we have reassured each other on very recently.

My question is, how can I best manage this situation going forward?

TLDR: New girlfriend has a ex as a close friend, they spent a lot of time together when she was back home and he sent an ambiguous message which hinted at more than friendship and now im torned on how to approach this.